Two classes of special functions using Fourier transforms of some finite classes of classical orthogonal polynomials |
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| Authors: | Wolfram Koepf Mohammad Masjed-Jamei |
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| Affiliation: | Department of Mathematics, University of Kassel, Heinrich-Plett-Str. 40, D-34132 Kassel, Germany ; Department of Mathematics, K. N. Toosi University of Technology, Sayed Khandan, Jolfa Av., Tehran, Iran |
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| Abstract: | Some orthogonal polynomial systems are mapped onto each other by the Fourier transform. The best-known example of this type is the Hermite functions, i.e., the Hermite polynomials multiplied by  , which are eigenfunctions of the Fourier transform. In this paper, we introduce two new examples of finite systems of this type and obtain their orthogonality relations. We also estimate a complicated integral and propose a conjecture for a further example of finite orthogonal sequences. |
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| Keywords: | Classical orthogonal polynomials Fourier transform hypergeometric functions Gosper identity Ramanujan integral |
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